FIA NLS Models: Biomass Growth vs. Stand Age
JAH
2023-04-21
Background
This document has nls (non-linear least squares) regression fits using the log-normal functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. stand age relationships. This functional form is commonly used in growth analyses, and permits a flexible shape to fit to data with an intermediate maximum (i.e., “hump” shaped) curve. As in our models of biomass growth vs. biomass, we use the mass balance biomass growth method for the plot biomass growth (\(G\)) calculation (briefly, plot biomass growth is a function of the change in plot biomass plus any losses due to mortality or harvest over time: \(G_{MB} = (\Delta B + M_t + C_t) / REMPER\), where \(\Delta B\) is change in plot biomass over a census interval ( \(\Delta B = B_{t + \Delta g} - B_t\) ), and \(M_t\) and \(C_t\) is the biomass of trees that died or were harvested, respectively, between two plot measurements. note: \(REMPER\) is time between two plot measurement intervals (FIA re-measurement period). For additional details see supplementary methods. Models are fitted separately by US ecoprovince.
Hypothetically, the entire functional form of the following non-linear model is considered: \(G = (1 + (yr-1990) \cdot tau/100) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(StdAge_{t1}\) is the FIA-estimated stand age at the first of two FIA plot tree censuses, and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(\tau\): the productivity trend, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(G\), \(c\): the \(StdAge_{t1}\) value at peak \(G\), and \(d\): the curve shape parameter.
Data have increasing variance in \(G\) with increasing \(StdAge_{t1}\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {StdAge_{t1}^2}\) in equal-sample sized plot biomass bins (n=20 where applicable, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.
Model selection is done to determine the best fitting models, considering the inclusion of \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest). Thus, the following two models are considered:
model 1: simple (tau) model \(G = (1 + (yr-1990) \cdot tau/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)
model 3: model \(G = (1 + (yr-1990) \cdot tau/100) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)
NOTE:
This document contains all \(G\) observations that meet our plot based filtering criteria:
- exclude FIA plots in plantation forests
- exclude FIA plots with multiple plot conditions (COND_PROG_UNADJ > 0.95)
- exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
- exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
- exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
- exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)
Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):
case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)
These data set cleaning criteria resulted in the exclusion of 1760 observations.
Below the model fitting procedure is implemented by ecoprovince:
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6869 2901.4
## 2 6817 2055.3 52 846.18 53.974 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 29461.42
## 2 2 26946.57##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.32590 0.17948 1.816 0.0694 .
## alpha 0.64710 0.03386 19.114 <2e-16 ***
## a 0.00000 2.44054 0.000 1.0000
## b 3.45262 2.42976 1.421 0.1554
## c 31.41828 2.14731 14.631 <2e-16 ***
## d 2.77428 1.17757 2.356 0.0185 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5491 on 6817 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (54 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
predict and plot
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 19351 8864.8
## 2 18862 4850.3 489 4014.5 31.926 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 83315.42
## 2 2 70488.69##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.75653 0.19895 8.829 < 2e-16 ***
## alpha 0.76060 0.02177 34.931 < 2e-16 ***
## a 0.86040 0.14171 6.072 1.29e-09 ***
## b 1.40974 0.13886 10.152 < 2e-16 ***
## c 21.80997 0.54644 39.913 < 2e-16 ***
## d 1.96787 0.15867 12.402 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5071 on 18862 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3847 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
predict and plot
## Warning: Removed 45 rows containing missing values (`geom_point()`).
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7319 3437.6
## 2 7255 2945.2 64 492.4 18.952 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 34070.15
## 2 2 32734.85##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.59046 0.14350 -4.115 3.92e-05 ***
## alpha 0.76479 0.04016 19.046 < 2e-16 ***
## a 2.72598 0.70218 3.882 0.000104 ***
## b 1.86724 0.69894 2.672 0.007568 **
## c 37.80243 3.28134 11.520 < 2e-16 ***
## d 1.78115 0.50574 3.522 0.000431 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6372 on 7255 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (72 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
predict and plot
## Warning: Removed 6 rows containing missing values (`geom_point()`).
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5044 2430.6
## 2 4824 1032.0 220 1398.6 29.715 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 25434.95
## 2 2 20512.77##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.28597 0.25555 1.119 0.263
## alpha 0.75519 0.04617 16.357 < 2e-16 ***
## a 1.83111 0.29293 6.251 4.43e-10 ***
## b 1.47931 0.28426 5.204 2.03e-07 ***
## c 48.40459 3.83860 12.610 < 2e-16 ***
## d 1.75565 0.31800 5.521 3.55e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4625 on 4824 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1015 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
predict and plot
## Warning: Removed 7 rows containing missing values (`geom_point()`).
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8872 4043.6
## 2 8730 2553.3 142 1490.3 35.883 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 41571.02
## 2 2 37049.42##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.43007 0.13891 -3.096 0.00197 **
## alpha 0.61024 0.04351 14.025 < 2e-16 ***
## a 1.93241 0.63204 3.057 0.00224 **
## b 1.92173 0.62274 3.086 0.00204 **
## c 27.16683 1.99950 13.587 < 2e-16 ***
## d 1.71082 0.42581 4.018 5.92e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5408 on 8730 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1274 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
predict and plot
## Warning: Removed 6 rows containing missing values (`geom_point()`).
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13446 7694.3
## 2 13195 6476.7 251 1217.6 9.8832 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 70330.21
## 2 2 67127.47##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.16093 0.16727 6.941 4.09e-12 ***
## alpha 0.88288 0.02005 44.035 < 2e-16 ***
## a 2.23956 0.21991 10.184 < 2e-16 ***
## b 2.99104 0.21013 14.234 < 2e-16 ***
## c 17.69249 0.40947 43.209 < 2e-16 ***
## d 1.47519 0.10215 14.441 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7006 on 13195 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (316 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
predict and plot
## Warning: Removed 30 rows containing missing values (`geom_point()`).
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13504 9637.4
## 2 13221 8286.2 283 1351.2 7.6181 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 70511.84
## 2 2 67419.32##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.24859 0.19228 6.494 8.68e-11 ***
## alpha 0.87949 0.01947 45.179 < 2e-16 ***
## a 2.94637 0.11008 26.766 < 2e-16 ***
## b 2.14747 0.10445 20.561 < 2e-16 ***
## c 15.79158 0.43175 36.576 < 2e-16 ***
## d 0.89719 0.05082 17.654 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7917 on 13221 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (402 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
predict and plot
## Warning: Removed 66 rows containing missing values (`geom_point()`).
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Error in nls(fg2_1, data = G_234, start = c(tau = tau.start, a = a.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 1 NA
## 2 2 6970.096##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 1.49367 0.96311 1.551 0.121170
## alpha 0.81742 0.08555 9.555 < 2e-16 ***
## a 3.25287 0.53212 6.113 1.29e-09 ***
## b 1.60897 0.49513 3.250 0.001185 **
## c 17.83130 2.52177 7.071 2.49e-12 ***
## d 0.68238 0.20357 3.352 0.000825 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8151 on 1316 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (66 observations deleted due to missingness)summary
- simple tau model: does not fit
- alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.90233, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.3394, p-value = 9.324e-08
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 5 rows containing missing values (`geom_point()`).
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1888 981.71
## 2 1773 366.60 115 615.11 25.868 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9553.901
## 2 2 7360.029##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.7210 0.5093 1.416 0.157072
## alpha 0.3998 0.1042 3.837 0.000129 ***
## a 0.0000 7.2404 0.000 1.000000
## b 2.6602 7.2394 0.367 0.713317
## c 29.1039 7.9249 3.672 0.000247 ***
## d 4.0010 6.4842 0.617 0.537291
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4547 on 1773 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (516 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.8207, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -8.0169, p-value = 1.085e-15
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 2 rows containing missing values (`geom_point()`).
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 710 1009.74
## 2 667 883.04 43 126.7 2.2256 1.96e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3560.631
## 2 2 3320.684##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 2.6192 2.2996 1.139 0.255118
## alpha 0.6898 0.1649 4.183 3.26e-05 ***
## a 0.6449 0.5334 1.209 0.227051
## b 1.9683 0.7959 2.473 0.013639 *
## c 15.9536 1.9433 8.210 1.15e-15 ***
## d 1.3146 0.3969 3.312 0.000975 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.151 on 667 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (44 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92514, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.8381, p-value = 0.000124
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 2 rows containing missing values (`geom_point()`).
plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
262 - California Dry Steppe
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
313 - Colorado Plateau Semi-Desert
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
322 - American Semidesert and Desert
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
331 - Great Plains/Palouse Dry Steppe
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
332 - Great Plains Steppe
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
341 - Intermountain Semi-desert & Desert
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
342 - Intermountain Semi-Desert
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
411 - Everglades
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6765 1889.9
## 2 6741 1757.0 24 132.81 21.23 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 25839.54
## 2 2 25285.87##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.91021 0.21562 4.221 2.46e-05 ***
## alpha 0.63388 0.02892 21.920 < 2e-16 ***
## a 2.41117 0.18853 12.789 < 2e-16 ***
## b 0.72219 0.14719 4.907 9.48e-07 ***
## c 30.21358 2.16166 13.977 < 2e-16 ***
## d 1.07272 0.25230 4.252 2.15e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5105 on 6741 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (25 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
predict and plot
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8308 4863.8
## 2 8253 4464.8 55 398.96 13.408 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 40946.90
## 2 2 40030.35##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.37987 0.19436 1.955 0.0507 .
## alpha 0.83193 0.05618 14.808 < 2e-16 ***
## a 2.83739 0.30722 9.236 < 2e-16 ***
## b 1.56703 0.25993 6.029 1.73e-09 ***
## c 26.79044 2.06992 12.943 < 2e-16 ***
## d 1.19017 0.24158 4.927 8.53e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7355 on 8253 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (56 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
predict and plot
## Warning: Removed 2 rows containing missing values (`geom_point()`).
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 890 537.81
## 2 883 515.61 7 22.204 5.4323 4.052e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3747.851
## 2 2 3694.417##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 3.8819 1.9304 2.011 0.044634 *
## alpha 0.8919 0.1493 5.976 3.32e-09 ***
## a 1.3980 0.3283 4.258 2.28e-05 ***
## b 0.8741 0.3169 2.758 0.005932 **
## c 32.1841 2.9862 10.778 < 2e-16 ***
## d 0.3997 0.1132 3.532 0.000433 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7641 on 883 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (7 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9565, p-value = 1.42e-15
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.926, p-value = 0.05411
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1000 560.60
## 2 987 494.92 13 65.684 10.076 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4301.062
## 2 2 4134.044##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 4.7642 2.3590 2.020 0.043700 *
## alpha 0.8568 0.1006 8.512 < 2e-16 ***
## a 1.2946 0.3543 3.654 0.000272 ***
## b 0.8329 0.2994 2.782 0.005497 **
## c 9.3076 4.1644 2.235 0.025636 *
## d 1.2870 0.5699 2.258 0.024155 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7081 on 987 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (13 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96666, p-value = 2.644e-14
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.1024, p-value = 1.045e-09
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M242 - Cascade Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3140 2646.7
## 2 3127 2508.0 13 138.76 13.308 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 17325.39
## 2 2 17112.54##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -1.58025 0.29550 -5.348 9.54e-08 ***
## alpha 1.00476 0.07301 13.761 < 2e-16 ***
## a 6.39200 0.59569 10.730 < 2e-16 ***
## b 4.91557 0.91371 5.380 8.01e-08 ***
## c 34.09178 1.56232 21.821 < 2e-16 ***
## d 0.33514 0.05330 6.288 3.67e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8956 on 3127 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (91 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92845, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -13.966, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 14 rows containing missing values (`geom_point()`).
plotting 2
M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1681 601.84
## 2 1668 585.67 13 16.172 3.543 1.672e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 8778.075
## 2 2 8686.805##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -2.4098 0.2443 -9.864 < 2e-16 ***
## alpha 0.6694 0.1103 6.071 1.57e-09 ***
## a 7.0661 0.6834 10.340 < 2e-16 ***
## b 7.5903 1.4855 5.109 3.60e-07 ***
## c 31.6516 1.0663 29.684 < 2e-16 ***
## d 0.2004 0.0429 4.671 3.24e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5926 on 1668 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (303 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.90125, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.018, p-value = 0.002544
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 9 rows containing missing values (`geom_point()`).
plotting 2
M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 360 174.32
## 2 359 168.10 1 6.2251 13.295 0.0003055 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 1014.707
## 2 2 1003.435##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -2.4926 0.3002 -8.304 2.08e-15 ***
## alpha 0.5805 0.1477 3.931 0.000101 ***
## a 0.0000 5.0587 0.000 1.000000
## b 3.3501 5.1050 0.656 0.512094
## c 61.8681 17.6811 3.499 0.000526 ***
## d 2.0796 2.2905 0.908 0.364526
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6843 on 359 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94781, p-value = 4.677e-10
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.2182, p-value = 0.2232
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1736 1579.8
## 2 1719 1424.7 17 155.19 11.014 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 5243.073
## 2 2 5045.153##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.59259 0.66774 -0.887 0.374960
## alpha 0.59000 0.06342 9.303 < 2e-16 ***
## a 0.40569 0.52551 0.772 0.440223
## b 1.39910 0.54744 2.556 0.010683 *
## c 50.60447 3.98505 12.699 < 2e-16 ***
## d 1.80430 0.53739 3.358 0.000804 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9104 on 1719 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (31 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.85792, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.2459, p-value = 1.556e-07
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 7 rows containing missing values (`geom_point()`).
plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2527 1847.2
## 2 2485 1678.8 42 168.39 5.9346 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9333.635
## 2 2 9043.297## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df2$Code == "M332", , value =
## structure(list(: provided 26 variables to replace 25 variables##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -0.64336 0.53013 -1.214 0.225020
## alpha 0.83163 0.05528 15.044 < 2e-16 ***
## a 0.72335 0.62864 1.151 0.249979
## b 1.82606 0.66347 2.752 0.005961 **
## c 61.15631 5.70900 10.712 < 2e-16 ***
## d 2.11186 0.57703 3.660 0.000258 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8219 on 2485 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (121 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.88303, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.6064, p-value = 3.938e-11
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 28 rows containing missing values (`geom_point()`).
plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1699 872.98
## 2 1670 777.35 29 95.626 7.084 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6978.661
## 2 2 6735.140##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau 0.09865 0.86145 0.115 0.909
## alpha 0.85743 0.05817 14.741 < 2e-16 ***
## a 1.42786 0.29092 4.908 1.01e-06 ***
## b 2.32526 0.45714 5.087 4.06e-07 ***
## c 49.89803 2.07205 24.081 < 2e-16 ***
## d 1.08912 0.09906 10.995 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6823 on 1670 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (77 observations deleted due to missingness)summary
- simple tau model: fits
- alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93058, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.5801, p-value = 2.403e-08
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 14 rows containing missing values (`geom_point()`).
plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Error in nls(fg2_1, data = G_M334, start = c(tau = tau.start, a = a.start, :
## Convergence failure: singular convergence (7)
## model AIC
## 1 1 NA
## 2 2 1382.769##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * tau/100) * (1 -
## alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## tau -3.4667 0.1424 -24.338 < 2e-16 ***
## alpha 0.7898 0.1840 4.293 2.28e-05 ***
## a 0.0000 1103.7169 0.000 1.000
## b 4.0869 1103.4463 0.004 0.997
## c 55.7353 113.2223 0.492 0.623
## d 4.9145 686.6947 0.007 0.994
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4695 on 349 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (104 observations deleted due to missingness)summary
- simple tau model: does not fit
- alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91466, p-value = 2.652e-13
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.8005, p-value = 0.07178
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing missing values (`geom_point()`).
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple tau model: does not fit
- alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 2 |
| 212 | Laurentian Mixed Forest | 2 |
| 221 | Eastern Broadleaf Forest | 2 |
| 222 | Midwest Broadleaf Forest | 2 |
| 223 | Central Interior Broadleaf Forest | 2 |
| 231 | Southeastern Mixed Forest | 2 |
| 232 | Outer Coastal Plain Mixed Forest | 2 |
| 234 | Lower Mississippi Riverine Forest | 2 |
| 242 | Pacific Lowland Mixed Forest | NA |
| 251 | Prairie Parkland (Temperate) | 2 |
| 255 | Prairie Parkland (Subtropical) | 2 |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA |
| 313 | Colorado Plateau Semi-Desert | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA |
| 332 | Great Plains Steppe | NA |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | NA |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 2 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 2 |
| M223 | Ozark Broadleaf Forest Meadow | 2 |
| M231 | Ouachita Mixed Forest | 2 |
| M242 | Cascade Mixed Forest | 2 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 2 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 2 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 2 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2 |
| M334 | Black Hills Coniferous Forest | 2 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | tau | tau.variance | tau.2.5 | tau.97.5 | alpha | alpha.variance | alpha.2.5 | alpha.97.5 | a | a.2.5 | a.97.5 | b | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6877 | 2876 | 0.3259037 | 0.0322117 | -0.0259256 | 0.6777330 | 0.6470960 | 0.0011462 | 0.5807292 | 0.7134629 | 0.0000000 | -4.7842150 | 4.784215 | 3.4526191 | -1.3104633 | 8.215701 | 31.418283 | 27.208885 | 35.62768 | 2.7742751 | 0.4658626 | 5.0826875 |
| 212 | Laurentian Mixed Forest | east | 22715 | 9499 | 1.7565265 | 0.0395794 | 1.3665749 | 2.1464782 | 0.7606008 | 0.0004741 | 0.7179210 | 0.8032805 | 0.8604044 | 0.5826362 | 1.138173 | 1.4097375 | 1.1375575 | 1.681918 | 21.809974 | 20.738898 | 22.88105 | 1.9678736 | 1.6568644 | 2.2788829 |
| 221 | Eastern Broadleaf Forest | east | 7333 | 3571 | -0.5904555 | 0.0205932 | -0.8717637 | -0.3091473 | 0.7647928 | 0.0016125 | 0.6860759 | 0.8435098 | 2.7259833 | 1.3494989 | 4.102468 | 1.8672377 | 0.4971107 | 3.237365 | 37.802432 | 31.370059 | 44.23481 | 1.7811498 | 0.7897481 | 2.7725515 |
| 222 | Midwest Broadleaf Forest | east | 5845 | 2589 | 0.2859672 | 0.0653067 | -0.2150307 | 0.7869651 | 0.7551947 | 0.0021316 | 0.6646816 | 0.8457078 | 1.8311146 | 1.2568301 | 2.405399 | 1.4793082 | 0.9220371 | 2.036579 | 48.404588 | 40.879181 | 55.93000 | 1.7556482 | 1.1322300 | 2.3790665 |
| 223 | Central Interior Broadleaf Forest | east | 10010 | 3864 | -0.4300667 | 0.0192949 | -0.7023555 | -0.1577778 | 0.6102431 | 0.0018932 | 0.5249506 | 0.6955356 | 1.9324112 | 0.6934665 | 3.171356 | 1.9217261 | 0.7010148 | 3.142437 | 27.166828 | 23.247331 | 31.08633 | 1.7108213 | 0.8761331 | 2.5455096 |
| 231 | Southeastern Mixed Forest | east | 13517 | 6193 | 1.1609328 | 0.0279784 | 0.8330644 | 1.4888011 | 0.8828828 | 0.0004020 | 0.8435823 | 0.9221832 | 2.2395602 | 1.8085049 | 2.670615 | 2.9910358 | 2.5791515 | 3.402920 | 17.692491 | 16.889878 | 18.49510 | 1.4751865 | 1.2749547 | 1.6754184 |
| 232 | Outer Coastal Plain Mixed Forest | east | 13629 | 6626 | 1.2485936 | 0.0369726 | 0.8716922 | 1.6254949 | 0.8794887 | 0.0003790 | 0.8413311 | 0.9176462 | 2.9463741 | 2.7306069 | 3.162141 | 2.1474654 | 1.9427364 | 2.352194 | 15.791585 | 14.945296 | 16.63787 | 0.8971916 | 0.7975747 | 0.9968085 |
| 234 | Lower Mississippi Riverine Forest | east | 1388 | 778 | 1.4936716 | 0.9275815 | -0.3957277 | 3.3830708 | 0.8174228 | 0.0073191 | 0.6495898 | 0.9852558 | 3.2528661 | 2.2089608 | 4.296771 | 1.6089700 | 0.6376478 | 2.580292 | 17.831300 | 12.884170 | 22.77843 | 0.6823767 | 0.2830100 | 1.0817435 |
| 242 | Pacific Lowland Mixed Forest | pacific | 83 | 83 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 2295 | 906 | 0.7210120 | 0.2594249 | -0.2779536 | 1.7199776 | 0.3998419 | 0.0108569 | 0.1954814 | 0.6042023 | 0.0000000 | -14.2005834 | 14.200583 | 2.6602066 | -11.5383913 | 16.858805 | 29.103890 | 13.560728 | 44.64705 | 4.0009667 | -8.7164867 | 16.7184201 |
| 255 | Prairie Parkland (Subtropical) | east | 717 | 319 | 2.6192087 | 5.2881553 | -1.8961158 | 7.1345333 | 0.6898464 | 0.0271917 | 0.3660624 | 1.0136304 | 0.6449176 | -0.4023978 | 1.692233 | 1.9683297 | 0.4056346 | 3.531025 | 15.953585 | 12.137853 | 19.76932 | 1.3145518 | 0.5352792 | 2.0938244 |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 25 | 25 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 163 | 161 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 218 | 218 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 331 | 255 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | interior west | 232 | 128 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 341 | Intermountain Semi-Desert and Desert | interior west | 66 | 64 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 124 | 123 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 96 | 63 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6772 | 3006 | 0.9102083 | 0.0464909 | 0.4875300 | 1.3328866 | 0.6338783 | 0.0008363 | 0.5771893 | 0.6905674 | 2.4111710 | 2.0415978 | 2.780744 | 0.7221916 | 0.4336594 | 1.010724 | 30.213582 | 25.976035 | 34.45113 | 1.0727185 | 0.5781330 | 1.5673041 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8315 | 3810 | 0.3798738 | 0.0377742 | -0.0011127 | 0.7608604 | 0.8319284 | 0.0031565 | 0.7217958 | 0.9420611 | 2.8373866 | 2.2351488 | 3.439624 | 1.5670342 | 1.0574968 | 2.076572 | 26.790440 | 22.732867 | 30.84801 | 1.1901696 | 0.7166178 | 1.6637213 |
| M223 | Ozark Broadleaf Forest Meadow | east | 896 | 349 | 3.8819227 | 3.7264172 | 0.0932287 | 7.6706166 | 0.8919471 | NA | 0.5990109 | 1.1848834 | 1.3979504 | 0.7536441 | 2.042257 | 0.8741302 | 0.2521252 | 1.496135 | 32.184123 | 26.323219 | 38.04503 | 0.3997004 | 0.1776253 | 0.6217755 |
| M231 | Ouachita Mixed Forest | east | 1006 | 495 | 4.7641593 | 5.5649730 | 0.1348893 | 9.3934294 | 0.8567699 | 0.0101303 | 0.6592587 | 1.0542812 | 1.2946131 | 0.5992694 | 1.989957 | 0.8329473 | 0.2455061 | 1.420388 | 9.307643 | 1.135637 | 17.47965 | 1.2869754 | 0.1685609 | 2.4053899 |
| M242 | Cascade Mixed Forest | pacific | 3224 | 3207 | -1.5802457 | 0.0873175 | -2.1596302 | -1.0008612 | 1.0047559 | 0.0053311 | 0.8615956 | 1.1479162 | 6.3920015 | 5.2240166 | 7.559986 | 4.9155744 | 3.1240373 | 6.707111 | 34.091781 | 31.028497 | 37.15506 | 0.3351390 | 0.2306335 | 0.4396445 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 1977 | 1807 | -2.4098383 | 0.0596808 | -2.8889984 | -1.9306782 | 0.6693505 | 0.0121571 | 0.4530890 | 0.8856120 | 7.0660557 | 5.7257203 | 8.406391 | 7.5902562 | 4.6765352 | 10.503977 | 31.651571 | 29.560209 | 33.74293 | 0.2003562 | 0.1162179 | 0.2844944 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 30 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 367 | 367 | -2.4926099 | 0.0901117 | -3.0829541 | -1.9022657 | 0.5805356 | 0.0218076 | 0.2901208 | 0.8709505 | 0.0000000 | -9.9484618 | 9.948462 | 3.3501089 | -6.6894500 | 13.389668 | 61.868141 | 27.096554 | 96.63973 | 2.0796397 | -2.4249124 | 6.5841918 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 1756 | 1756 | -0.5925858 | 0.4458749 | -1.9022516 | 0.7170800 | 0.5899990 | 0.0040224 | 0.4656051 | 0.7143929 | 0.4056943 | -0.6250198 | 1.436408 | 1.3990983 | 0.3253788 | 2.472818 | 50.604467 | 42.788414 | 58.42052 | 1.8042968 | 0.7502961 | 2.8582975 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 2612 | 2602 | -0.6433640 | 0.2810415 | -1.6829128 | 0.3961848 | 0.8316342 | 0.0030560 | 0.7232333 | 0.9400351 | 0.7233522 | -0.5093529 | 1.956057 | 1.8260584 | 0.5250439 | 3.127073 | 61.156314 | 49.961419 | 72.35121 | 2.1118589 | 0.9803577 | 3.2433601 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 1753 | 1742 | 0.0986515 | 0.7421010 | -1.5909896 | 1.7882926 | 0.8574276 | 0.0033834 | 0.7433405 | 0.9715147 | 1.4278560 | 0.8572552 | 1.998457 | 2.3252552 | 1.4286291 | 3.221881 | 49.898029 | 45.833939 | 53.96212 | 1.0891217 | 0.8948317 | 1.2834117 |
| M334 | Black Hills Coniferous Forest | interior west | 459 | 181 | -3.4667353 | 0.0202887 | -3.7468811 | -3.1865895 | 0.7897504 | 0.0338387 | 0.4279547 | 1.1515460 | 0.0000000 | -2170.7734030 | 2170.773403 | 4.0869419 | -2166.1541718 | 2174.328056 | 55.735252 | -166.948614 | 278.41912 | 4.9144979 | -1345.6661082 | 1355.4951039 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 220 | 220 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
parameter variance co-variance
## png
## 2plot tau
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I## Warning: package 'ggnewscale' was built under R version 4.2.1## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation ideoms with `aes()`## Warning: The `size` argument of `element_line()` is deprecated as of ggplot2 3.4.0.
## ℹ Please use the `linewidth` argument instead.## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
plot alpha (biomass growth compensation effect)
plot a coefficient
## Warning: Removed 15 rows containing missing values (`geom_point()`).
plot b coefficient
## Warning: Removed 15 rows containing missing values (`geom_point()`).
plot c coefficient
## Warning: Removed 1 rows containing missing values (`geom_hline()`).## Warning: Removed 16 rows containing missing values (`geom_point()`).
plot d coefficient
## Warning: Removed 15 rows containing missing values (`geom_point()`).
Caclulations - weighted averages
tau (productivity trend (in %) 2000-2022)
## region weighted.tau weighted.tau.std_Error 95 % CI, upper
## 1 entire US 0.46776517 0.07376303 0.612340704
## 2 pacific -0.16266596 0.01804796 -0.127291955
## 3 east 0.70095388 0.05885088 0.816301604
## 4 interior west -0.07052274 0.04064270 0.009136941
## 95 % CI, lower
## 1 0.3231896
## 2 -0.1980400
## 3 0.5856061
## 4 -0.1501824alpha (biomass growth compensation effect)
## region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1 entire US 0.75849014 0.010377384 0.77882982
## 2 pacific 0.07650874 0.005307716 0.08691186
## 3 east 0.59480677 0.008086378 0.61065607
## 4 interior west 0.08717463 0.003758821 0.09454192
## 95 % CI, lower
## 1 0.73815047
## 2 0.06610561
## 3 0.57895747
## 4 0.07980735